feat: SM-2 + 페르소나 하이브리드 복습 알고리즘

- SM-2 Easiness Factor + 페르소나별 망각속도 보정 (senior 1.3x ~ crammer 0.6x) - 최초 학습(iter=0): hard=1d, medium=3d, easy=7d 차등 간격 - 2회차~: 반복할수록 간격 증가 (6 × EF^(iter-1) × pf) - hard → EF 하락 + 간격 리셋(1일), easy → EF 상승 + 간격 확대 - EF 는 SkillSnapshot.s0 에 저장 (태그별 개인 학습 용이도) - 프론트 3버튼에 SM-2 기반 동적 간격 미리보기 표시 - 기존 PersonaForgetService.schedule/updateS0 유지 (selfDifficulty 없는 경우 fallback) Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
2026-04-16 15:31:47 +09:00
parent 25092bf680
commit 8aa87ed257
5 changed files with 284 additions and 109 deletions
--- a/backend/src/forget/persona-forget.service.ts
+++ b/backend/src/forget/persona-forget.service.ts
@@ -38,6 +38,34 @@ export const PERSONA_LAMBDA: Record<Persona, number> = {
  crammer: 0.6,
 };

+// ── SM-2 Hybrid ──────────────────────────────────────────────────────────────
+
+export const PERSONA_FACTOR: Record<Persona, number> = {
+  senior: 1.3,
+  mid: 1.0,
+  junior: 0.8,
+  crammer: 0.6,
+};
+
+export const DEFAULT_EF = 2.5;
+export const MIN_EF = 1.3;
+
+export type SelfDifficulty = 'hard' | 'medium' | 'easy';
+
+export interface SM2Input {
+  iteration: number;
+  selfDifficulty: SelfDifficulty;
+  currentEF: number;
+  persona: Persona;
+  now?: Date;
+}
+
+export interface SM2Output {
+  intervalDays: number;
+  newEF: number;
+  scheduledAt: Date;
+}
+
 export const INTENSITY_THRESHOLD: Record<ReviewIntensity, number> = {
  strict: 0.7,
  moderate: 0.5,
@@ -183,6 +211,69 @@ export class PersonaForgetService {
    return points;
  }

+  /**
+   * SM-2 + 페르소나 하이브리드 스케줄러.
+   *
+   * iteration=0 (최초 학습):
+   *   hard   → 1일
+   *   medium → round(3 × pf)일
+   *   easy   → round(7 × pf)일
+   *
+   * iteration=1 (첫 복습):
+   *   hard   → 1일
+   *   else   → round(6 × pf)일
+   *
+   * iteration≥2:
+   *   hard   → 1일 (EF 하락 + 리셋)
+   *   else   → round(6 × EF^(iteration-1) × pf)일
+   *
+   * EF 업데이트:
+   *   hard   → max(MIN_EF, EF - 0.3)
+   *   easy   → max(MIN_EF, EF + 0.15)
+   *   medium → 변화 없음
+   *
+   * 결과는 [1, MAX_INTERVAL_DAYS] 범위로 클램핑.
+   */
+  sm2Schedule(input: SM2Input): SM2Output {
+    const { iteration, selfDifficulty, currentEF, persona } = input;
+    const now = input.now ?? new Date();
+    const pf = PERSONA_FACTOR[persona] ?? 1.0;
+
+    // EF 업데이트
+    let newEF = currentEF;
+    if (selfDifficulty === 'hard') {
+      newEF = Math.max(MIN_EF, currentEF - 0.3);
+    } else if (selfDifficulty === 'easy') {
+      newEF = Math.max(MIN_EF, currentEF + 0.15);
+    }
+
+    // 간격 계산
+    let intervalDays: number;
+    if (selfDifficulty === 'hard') {
+      intervalDays = 1;
+    } else if (iteration <= 0) {
+      // 최초 학습 — selfDifficulty 에 따라 차등
+      if (selfDifficulty === 'medium') {
+        intervalDays = Math.round(3 * pf);
+      } else {
+        // easy
+        intervalDays = Math.round(7 * pf);
+      }
+    } else if (iteration === 1) {
+      intervalDays = Math.round(6 * pf);
+    } else {
+      intervalDays = Math.round(6 * Math.pow(newEF, iteration - 1) * pf);
+    }
+
+    intervalDays = Math.max(1, Math.min(MAX_INTERVAL_DAYS, intervalDays));
+
+    return {
+      intervalDays,
+      newEF,
+      scheduledAt: addDays(now, intervalDays),
+    };
+  }
+
  sigmoid(x: number): number {
    return 1 / (1 + Math.exp(-x));
  }
--- a/backend/src/reviews/reviews.service.ts
+++ b/backend/src/reviews/reviews.service.ts
@@ -6,7 +6,7 @@ import {
 } from '@nestjs/common';
 import { StudyResult, ReviewStatus } from '@prisma/client';
 import { PrismaService } from '../prisma/prisma.service';
-import { PersonaForgetService } from '../forget/persona-forget.service';
+import { PersonaForgetService, DEFAULT_EF } from '../forget/persona-forget.service';

@Injectable()
 export class ReviewsService {
@@ -89,58 +89,96 @@ export class ReviewsService {
        where: { id: reviewId },
      });

-      // b/c. Snapshot upsert inside tx
-      let newS0: number;
-      if (review.studyLog.tagId) {
-        const existing = await tx.skillSnapshot.findUnique({
-          where: {
-            userId_tagId: { userId, tagId: review.studyLog.tagId },
-          },
-        });
-        newS0 = this.forget.updateS0({
-          previousS0: existing?.s0 ?? null,
-          result,
-          baseCorrectRate: review.studyLog.baseCorrectRate ?? undefined,
-        });
-        await tx.skillSnapshot.upsert({
-          where: {
-            userId_tagId: { userId, tagId: review.studyLog.tagId },
-          },
-          create: {
-            userId,
-            tagId: review.studyLog.tagId,
-            s0: newS0,
-            lastUpdatedAt: now,
-            sampleCount: 1,
-          },
-          update: {
-            s0: newS0,
-            lastUpdatedAt: now,
-            sampleCount: { increment: 1 },
-          },
-        });
-      } else {
-        newS0 = this.forget.updateS0({
-          previousS0: null,
-          result,
-          baseCorrectRate: review.studyLog.baseCorrectRate ?? undefined,
-        });
-      }
-
-      // d. Compute next schedule
-      const SELF_DIFFICULTY_DAYS: Record<string, number> = {
-        hard: 1,
-        medium: 7,
-        easy: 30,
-      };
-
+      // b/c. Snapshot upsert + next schedule (SM-2 or legacy)
      let nextScheduledAt: Date;
      let nextPredictedP: number | null = null;

+      // e. Fetch the true latest iteration for this studyLog inside tx
+      const lastDone = await tx.reviewSchedule.findFirst({
+        where: { studyLogId: review.studyLogId, status: 'done' },
+        orderBy: { iteration: 'desc' },
+      });
+      const nextIteration = (lastDone?.iteration ?? flipped.iteration) + 1;
+
      if (selfDifficulty) {
-        const days = SELF_DIFFICULTY_DAYS[selfDifficulty];
-        nextScheduledAt = new Date(now.getTime() + days * 24 * 3_600_000);
+        // ── SM-2 하이브리드 경로 ──────────────────────────────────────────────
+        let currentEF = DEFAULT_EF;
+        if (review.studyLog.tagId) {
+          const snap = await tx.skillSnapshot.findUnique({
+            where: { userId_tagId: { userId, tagId: review.studyLog.tagId } },
+          });
+          if (snap && snap.s0 >= 1.3 && snap.s0 <= 4.0) {
+            currentEF = snap.s0;
+          }
+        }
+
+        const sm2 = this.forget.sm2Schedule({
+          iteration: nextIteration,
+          selfDifficulty,
+          currentEF,
+          persona: user.persona,
+          now,
+        });
+        nextScheduledAt = sm2.scheduledAt;
+        nextPredictedP = null;
+
+        // EF 업데이트: tagId 있는 경우 저장
+        if (review.studyLog.tagId) {
+          await tx.skillSnapshot.upsert({
+            where: { userId_tagId: { userId, tagId: review.studyLog.tagId } },
+            create: {
+              userId,
+              tagId: review.studyLog.tagId,
+              s0: sm2.newEF,
+              lastUpdatedAt: now,
+              sampleCount: nextIteration,
+            },
+            update: {
+              s0: sm2.newEF,
+              lastUpdatedAt: now,
+              sampleCount: nextIteration,
+            },
+          });
+        }
      } else {
+        // ── 기존 망각곡선 경로 (selfDifficulty 없는 경우) ────────────────────
+        let newS0: number;
+        if (review.studyLog.tagId) {
+          const existing = await tx.skillSnapshot.findUnique({
+            where: {
+              userId_tagId: { userId, tagId: review.studyLog.tagId },
+            },
+          });
+          newS0 = this.forget.updateS0({
+            previousS0: existing?.s0 ?? null,
+            result,
+            baseCorrectRate: review.studyLog.baseCorrectRate ?? undefined,
+          });
+          await tx.skillSnapshot.upsert({
+            where: {
+              userId_tagId: { userId, tagId: review.studyLog.tagId },
+            },
+            create: {
+              userId,
+              tagId: review.studyLog.tagId,
+              s0: newS0,
+              lastUpdatedAt: now,
+              sampleCount: 1,
+            },
+            update: {
+              s0: newS0,
+              lastUpdatedAt: now,
+              sampleCount: { increment: 1 },
+            },
+          });
+        } else {
+          newS0 = this.forget.updateS0({
+            previousS0: null,
+            result,
+            baseCorrectRate: review.studyLog.baseCorrectRate ?? undefined,
+          });
+        }
+
        const schedule = this.forget.schedule({
          s0: newS0,
          persona: user.persona,
@@ -152,13 +190,6 @@ export class ReviewsService {
        nextPredictedP = schedule.predictedP;
      }

-      // e. Fetch the true latest iteration for this studyLog inside tx
-      const lastDone = await tx.reviewSchedule.findFirst({
-        where: { studyLogId: review.studyLogId, status: 'done' },
-        orderBy: { iteration: 'desc' },
-      });
-      const nextIteration = (lastDone?.iteration ?? flipped.iteration) + 1;
-
      // f. Insert next review row
      const nextRow = await tx.reviewSchedule.create({
        data: {
@@ -171,7 +202,7 @@ export class ReviewsService {
        },
      });

-      return { updated: flipped, nextReview: nextRow, s0: newS0 };
+      return { updated: flipped, nextReview: nextRow };
    });

    return txResult;
--- a/backend/src/study-logs/study-logs.service.ts
+++ b/backend/src/study-logs/study-logs.service.ts
@@ -12,7 +12,7 @@ import {
  StudyResult,
 } from "@prisma/client";
 import { PrismaService } from "../prisma/prisma.service";
-import { PersonaForgetService } from "../forget/persona-forget.service";
+import { PersonaForgetService, DEFAULT_EF } from "../forget/persona-forget.service";

 export interface CreateStudyLogInput {
  subjectId: number;
@@ -551,53 +551,86 @@ export class StudyLogsService {
      },
    });

-    let s0 = 0.3;
-    if (input.tagId) {
-      const existing = await tx.skillSnapshot.findUnique({
-        where: { userId_tagId: { userId, tagId: input.tagId } },
-      });
-      const prevS0 = existing?.s0 ?? null;
-      s0 = this.forget.updateS0({
-        previousS0: prevS0,
-        result: input.result,
-        baseCorrectRate: input.baseCorrectRate ?? undefined,
-      });
-      await tx.skillSnapshot.upsert({
-        where: { userId_tagId: { userId, tagId: input.tagId } },
-        create: {
-          userId,
-          tagId: input.tagId,
-          s0,
-          lastUpdatedAt: now,
-          sampleCount: 1,
-        },
-        update: {
-          s0,
-          lastUpdatedAt: now,
-          sampleCount: { increment: 1 },
-        },
-      });
-    } else {
-      s0 = this.forget.updateS0({
-        previousS0: null,
-        result: input.result,
-        baseCorrectRate: input.baseCorrectRate ?? undefined,
-      });
-    }
-
-    const SELF_DIFFICULTY_DAYS: Record<string, number> = {
-      hard: 1,
-      medium: 7,
-      easy: 30,
-    };
-
    let scheduledAt: Date;
    let predictedP: number | null = null;

    if (input.selfDifficulty) {
-      const days = SELF_DIFFICULTY_DAYS[input.selfDifficulty];
-      scheduledAt = new Date(now.getTime() + days * 24 * 3_600_000);
+      // ── SM-2 하이브리드 경로 ────────────────────────────────────────────────
+      // tagId 있으면 SkillSnapshot.s0 에서 EF 로드 (EF 범위 1.3~4.0 이면 사용)
+      let currentEF = DEFAULT_EF;
+      if (input.tagId) {
+        const snap = await tx.skillSnapshot.findUnique({
+          where: { userId_tagId: { userId, tagId: input.tagId } },
+        });
+        if (snap && snap.s0 >= 1.3 && snap.s0 <= 4.0) {
+          currentEF = snap.s0;
+        }
+      }
+
+      const sm2 = this.forget.sm2Schedule({
+        iteration: 0,
+        selfDifficulty: input.selfDifficulty,
+        currentEF,
+        persona: user.persona,
+        now,
+      });
+      scheduledAt = sm2.scheduledAt;
+      predictedP = null;
+
+      // EF 저장: tagId 있는 경우 SkillSnapshot.s0 에 EF 값으로 upsert
+      if (input.tagId) {
+        await tx.skillSnapshot.upsert({
+          where: { userId_tagId: { userId, tagId: input.tagId } },
+          create: {
+            userId,
+            tagId: input.tagId,
+            s0: sm2.newEF,
+            lastUpdatedAt: now,
+            sampleCount: 1,
+          },
+          update: {
+            s0: sm2.newEF,
+            lastUpdatedAt: now,
+            sampleCount: { increment: 1 },
+          },
+        });
+      }
    } else {
+      // ── 기존 망각곡선 경로 (selfDifficulty 없는 경우) ────────────────────────
+      let s0 = 0.3;
+      if (input.tagId) {
+        const existing = await tx.skillSnapshot.findUnique({
+          where: { userId_tagId: { userId, tagId: input.tagId } },
+        });
+        const prevS0 = existing?.s0 ?? null;
+        s0 = this.forget.updateS0({
+          previousS0: prevS0,
+          result: input.result,
+          baseCorrectRate: input.baseCorrectRate ?? undefined,
+        });
+        await tx.skillSnapshot.upsert({
+          where: { userId_tagId: { userId, tagId: input.tagId } },
+          create: {
+            userId,
+            tagId: input.tagId,
+            s0,
+            lastUpdatedAt: now,
+            sampleCount: 1,
+          },
+          update: {
+            s0,
+            lastUpdatedAt: now,
+            sampleCount: { increment: 1 },
+          },
+        });
+      } else {
+        s0 = this.forget.updateS0({
+          previousS0: null,
+          result: input.result,
+          baseCorrectRate: input.baseCorrectRate ?? undefined,
+        });
+      }
+
      const schedule = this.forget.schedule({
        s0,
        persona: user.persona,
@@ -620,7 +653,7 @@ export class StudyLogsService {
      },
    });

-    return { studyLog: log, nextReview: reviewRow, s0 };
+    return { studyLog: log, nextReview: reviewRow };
  }
 }

--- a/frontend/src/app/exams/sample-ebook/[id]/page.tsx
+++ b/frontend/src/app/exams/sample-ebook/[id]/page.tsx
@@ -15,10 +15,12 @@ import type { SampleProblem } from '../data/types';

 type SelfDifficulty = 'hard' | 'medium' | 'easy';

-const SELF_DIFFICULTY_DAYS: Record<SelfDifficulty, number> = {
+// SM-2 기반 최초 학습(iteration=0) 간격 미리보기
+// 서버와 동일한 공식: persona_factor 는 클라이언트 미지이므로 pf=1.0 기준
+const INITIAL_INTERVAL_DAYS: Record<SelfDifficulty, number> = {
  hard: 1,
-  medium: 7,
-  easy: 30,
+  medium: 3,
+  easy: 7,
 };

 const DIFFICULTY_SCORE: Record<SampleProblem['difficulty'], number> = {
@@ -611,7 +613,7 @@ function EbookViewer({ id, title, grade, problems }: EbookViewerProps) {
                      >
                        <SelfEvalEmoji>🔴</SelfEvalEmoji>
                        <SelfEvalLabel>어려웠어</SelfEvalLabel>
-                        <SelfEvalInterval>1일 뒤</SelfEvalInterval>
+                        <SelfEvalInterval>{INITIAL_INTERVAL_DAYS.hard}일 뒤</SelfEvalInterval>
                      </SelfEvalButton>
                      <SelfEvalButton
                        type="button"
@@ -621,7 +623,7 @@ function EbookViewer({ id, title, grade, problems }: EbookViewerProps) {
                      >
                        <SelfEvalEmoji>🟡</SelfEvalEmoji>
                        <SelfEvalLabel>괜찮았어</SelfEvalLabel>
-                        <SelfEvalInterval>7일 뒤</SelfEvalInterval>
+                        <SelfEvalInterval>{INITIAL_INTERVAL_DAYS.medium}일 뒤</SelfEvalInterval>
                      </SelfEvalButton>
                      <SelfEvalButton
                        type="button"
@@ -631,7 +633,7 @@ function EbookViewer({ id, title, grade, problems }: EbookViewerProps) {
                      >
                        <SelfEvalEmoji>🟢</SelfEvalEmoji>
                        <SelfEvalLabel>쉬웠어</SelfEvalLabel>
-                        <SelfEvalInterval>30일 뒤</SelfEvalInterval>
+                        <SelfEvalInterval>{INITIAL_INTERVAL_DAYS.easy}일 뒤</SelfEvalInterval>
                      </SelfEvalButton>
                    </SelfEvalButtons>
                  </>
--- a/frontend/src/app/review/page.tsx
+++ b/frontend/src/app/review/page.tsx
@@ -29,6 +29,24 @@ import { animations, theme } from '@/styles/theme';

 type ReviewAction = 'hard' | 'medium' | 'easy' | 'skip';

+// SM-2 간격 미리보기 (클라이언트 측 근사값, 서버가 정확한 값 계산)
+// persona 를 모르므로 기본 pf=1.0, EF=2.5 기준
+const DEFAULT_EF_PREVIEW = 2.5;
+const MAX_INTERVAL_PREVIEW = 60;
+
+function previewIntervalDays(
+  iteration: number,
+  selfDifficulty: 'hard' | 'medium' | 'easy',
+): number {
+  if (selfDifficulty === 'hard') return 1;
+  if (iteration <= 0) {
+    return selfDifficulty === 'medium' ? 3 : 7;
+  }
+  if (iteration === 1) return 6;
+  const days = Math.round(6 * Math.pow(DEFAULT_EF_PREVIEW, iteration - 1));
+  return Math.max(1, Math.min(MAX_INTERVAL_PREVIEW, days));
+}
+
 const SELF_DIFFICULTY_RESULT: Record<'hard' | 'medium' | 'easy', StudyResult> = {
  hard: 'incorrect',
  medium: 'partial',
@@ -695,7 +713,7 @@ export default function ReviewPage() {
                <ActionLabel>
                  🔴 어려웠어
                </ActionLabel>
-                <ActionHelper>1일 뒤 다시 볼게</ActionHelper>
+                <ActionHelper>{previewIntervalDays(currentItem.iteration, 'hard')}일 뒤 다시 볼게</ActionHelper>
              </ActionCopy>
              <ActionShortcut>1</ActionShortcut>
            </ActionButton>
@@ -710,7 +728,7 @@ export default function ReviewPage() {
                <ActionLabel>
                  🟡 괜찮았어
                </ActionLabel>
-                <ActionHelper>7일 뒤 다시 볼게</ActionHelper>
+                <ActionHelper>{previewIntervalDays(currentItem.iteration, 'medium')}일 뒤 다시 볼게</ActionHelper>
              </ActionCopy>
              <ActionShortcut>2</ActionShortcut>
            </ActionButton>
@@ -725,7 +743,7 @@ export default function ReviewPage() {
                <ActionLabel>
                  🟢 쉬웠어
                </ActionLabel>
-                <ActionHelper>30일 뒤 다시 볼게</ActionHelper>
+                <ActionHelper>{previewIntervalDays(currentItem.iteration, 'easy')}일 뒤 다시 볼게</ActionHelper>
              </ActionCopy>
              <ActionShortcut>3</ActionShortcut>
            </ActionButton>